What distinguishes linear regression from correlation?

The distinguishing feature of linear regression compared to correlation is that linear regression is primarily used to make predictions about one variable based on another. In linear regression, you typically have an independent variable (predictor) and a dependent variable (outcome), and the method constructs a mathematical model that describes the relationship between these two variables. This allows for predictions about the dependent variable when given the independent variable.

In contrast, correlation measures the strength and direction of a linear relationship between two variables but does not imply causation or allow for prediction in the same way that linear regression does. While correlation provides a statistical measure (the correlation coefficient) that indicates how closely two variables move together, it does not create a model for predicting one variable based on the other.

The other options do not accurately represent a core difference between linear regression and correlation. For instance, while an r-squared value is related to regression analysis, it does not serve as a predictive tool in correlation. Linear regression primarily assesses linear relationships, and while it can sometimes be adapted to handle non-linear relationships (through transformations or polynomial regression), that is not its main focus or a distinguishing characteristic. Lastly, correlation is not designed for handling categorical data effectively, as it typically pertains to continuous numerical data.